Iraqi military officials insisted that safe corridors would be established to allow civilians to flee, but residents said ISIL checkpoints along the city's main roads have made escape nearly impossible.

"Our forces evacuated 460 people ... most of them women and children," police Lieutenant General Raed Shakir Jawdat said.

Tens of thousands of Iraqi forces - made up of military, police and militias, and backed by air power from a US-led coalition - last week launched an offensive to retake the city.

Fallujah, along with Mosul, is one of only two major Iraqi cities still controlled by ISIL, which is also known as ISIS. It became in January 2014 the first Iraqi city to be captured by the group, six months before it declared its caliphate.

General Saad Harbiya, head of Fallujah operations for the Iraqi army, said keeping civilians safe was a priority.

"Our plans are humanitarian plans," Harbiya said. "The most important thing is to get the civilians out unharmed."

Baghdad-based US Colonel Steve Warren said that over the last four days, 20 strikes in the city had destroyed ISIL fighting positions and gun emplacements.

"We've killed more than 70 enemy fighters, including Maher al-Bilawi, who is the commander of ISIL forces in Fallujah," Warren said.

"This, of course, won't completely cause the enemy to stop fighting, but it's a blow. And it creates confusion and it causes the second-in-command to have to move up. It causes other leadership to have to move around," he added.

Some in Fallujah, a predominantly Sunni city, were reported to have welcomed the takeover of the city by ISIL as an alternative to what they considered their marginalisation at the hands of Iraq's Shia-dominated government. Locals, though, say conditions there have deteriorated under the group's control.

Coalition officials estimated earlier this week that 500-700 ISIL fighters remain in the city, according to a US military estimate, hiding amongst the civilian population.

Located 65km west of Baghdad, Fallujah has a history of anti-government sentiment in post-2003 Iraq.

The city on the Euphrates River had a prewar population of about 300,000. Known as the City of Minarets and Mother of Mosques, it was badly damaged in two assaults by the US army against suspected al-Qaeda fighters in 2004.